Our place too is so dead-quiet it's like you can hear the cuckoos, and things are so tight we don't have the budget to hire any part-timers.

Literal

Our-place [also-だって] loneliness-bird [subject-が] sings [like-ような] barely-managing state is-[because-から], part-time-job [obj-を] hire leeway [something-like-なんて] don't-have.

Two idioms in quick succession. 閑古鳥が鳴く ('the quiet bird sings') is a fixed expression meaning 'a shop is dead, nobody's coming in' — 閑古鳥 is a literary/folk name for the cuckoo, whose solitary song marks isolation. カツカツ is a mimetic for 'barely making it, on the edge of what's possible.' バイト is the casual loan for 'part-time job' (from German 'Arbeit'). なんて here is a dismissive emphatic — 'no leeway, much less for hiring.' だって on ウチ means 'even [my place] / my place too.' A fluent, colloquial complaint full of learner-useful vocabulary.